About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Novo, Sébastien ; Novotný, Antonín
A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid. (English). Applications of Mathematics, vol. 50 (2005), issue 4, pp. 331-339
MSC: 35D05, 35Q30, 76N10 | MR 2151460 | Zbl 1099.35088 | DOI: 10.1007/s10492-005-0026-y
Keywords:
Navier-Stokes equations; compressible fluid; weak solution
Summary:
For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.
References:
[1] M. E.  Bogovskiĭ: The solution of some problems of vector analysis, associated with the operators div and grad. Trudy Semin. S. L.  Soboleva 1 (1980), 5–40. (Russian) MR 0631691
[2] R. J.  DiPerna, P.-L.  Lions: Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989), 511–547. DOI 10.1007/BF01393835 | MR 1022305
[3] L. C.  Evans, R. F.  Gariepy: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, 1992. MR 1158660
[4] P.-L.  Lions: Mathematical Topics in Fluid Mechanics, Vol.  2. Compressible Models. Lecture Series in Mathematics and its Applications. Clarendon Press, Oxford, 1998. MR 1637634
[5] S.  Novo, A.  Novotný: On the existence of weak solutions to the steady compressible Navier-Stokes equations when the density is not square integrable. J.  Math. Kyoto Univ. 42 (2002), 531–550. DOI 10.1215/kjm/1250283849 | MR 1967222
[6] S.  Novo, A.  Novotný: On the existence of weak solutions to the steady compressible Navier-Stokes equations in domains with conical outlets. J. Math. Fluid Mech. 7 (2005), 1–24. MR 2220444
Partner of
EuDML logo